When reading Justice Alito's majority opinion in Hobby Lobby alongside Justice Kennedy's concurring opinion, the unifying thread is clear. And the results don't bode well for the pending cases of religious non-profits against the HHS mandate.
A for-profit corproration has been granted its claim under the Religious Freedom Restoration Act (RFRA) only because Kennedy maintains that the government did not use the least restrictive means of providing its compelling interest. From Kennedy (p. 3):
The means the Government chose is the imposition of a direct mandate on the employers in these cases. ... But in other instances the Government has allowed the same contraception coverage in issue here to be provided to employees of nonprofit religious organizations, as an accommodation to the religious objections of those entities. ... The accommodation works by requiring insurance companies to cover, without cost sharing, contraception coverage for female employees who wish it. That accommodation equally furthers the Government’s interest but does not impinge on the plaintiffs’ religious beliefs.
HHS shouldn't distinguish between different religious believers, "when it may treat both equally by offering both of them the same accommodation." Later he repeats that "the mechanism for doing so is already in place." Thus the accommodation of religious non-profits currently on offer is precisely the legal model available for the for-profits (such as Hobby Lobby).
Justice Alito, for his part, makes similar points, but his opinion issues many more challenges to the government's case. The juxtaposition gives the sense that Kennedy was brought on board the majority only in so far as the "accommodation" option of the HHS mandate would be presented as a legal, alternative mechanism for delivering the government's compelling interest -- an interest Kennedy clearly believes the government has.
The suspicion that religious non-profits are not going to be exempted is perhaps corroborated by Alito's little scuffle in the footnotes about the fate of Little Sisters of the Poor for the Aged v. Sibelius (Alito n. 40 v. Ginsburg n. 27). That is to say, with today's ruling -- and presuming the same occupants of the court in the near future -- it is difficult if not impossible to see how religious non-profits such as Little Sisters of the Poor could win a RFRA claim.
In short, how could Alito and Kennedy rule in favor of Little Sisters of the Poor or other accommodated religious non-profits, when they said today that the accommodation model is the way forward for Hobby Lobby?
Nonetheless, there is still the matter of the self-certification form that would need to trigger the third-party coverage without cost-sharing. It remains to be seen whether the Roberts court finds the very act of conscientiously objecting through a piece of paper to be a "substantial burden" under RFRA. But based on the evidence of today's convergence between Alito and Kennedy, I don't think the accommodated non-profits can expect that burden to count.
UPDATE: I now note that Yuval Levin at National Review also reads Kennedy's concurrence in this way:
... it seems to me that Kennedy is here going out of his way to say that he thinks the mandate advances a compelling government interest and that the accommodation might be the least burdensome way to advance it. And those are not just random points to make: they speak to the two-pronged test set out by RFRA.
Of course, the administration’s proposed accommodation was not at issue in this case. No one briefed it or discussed it in detail, and when the plaintiff’s attorney was asked about it in oral argument he said it hadn’t been offered to his clients so he had no opinion about it. So there would be no reason for Kennedy to have reached a judgment on it, and he surely didn’t give it the consideration he would in a case in which the accommodation was directly at issue. But these lines in Kennedy’s concurring opinion do seem to involve his going to some lengths to say he may be open to it — and therefore that today’s majority may not hold when the Little Sisters of the Poor and other groups bring the question of the administration’s accommodation before the Court.